wip: check for divergence

Author: chentoast

src/inference/hmc_common.jl

@@ -8,4 +8,4 @@ function assess_momenta(momenta)
       logprob += logpdf(normal, val, 0, 1)
   end
   logprob
-end
+end

src/inference/nuts.jl

@@ -1,6 +1,6 @@
 using LinearAlgebra: dot
 
-Tree = @NamedTuple begin
+struct Tree
   val_left
   momenta_left
   val_right
@@ -9,9 +9,10 @@ Tree = @NamedTuple begin
   n :: Int
   weight :: Float64
   stop :: Bool
+  diverging :: Bool
 end
 
-Stats = @NamedTuple begin
+struct SamplerStats
   depth
   n
   accept
@@ -47,11 +48,13 @@ function leapfrog(values, momenta, eps, integrator_state)
   return values, momenta, get_score(trace)
 end
 
-function build_root(val, momenta, eps, direction, integrator_state)
+function build_root(val, momenta, eps, direction, weight_init, integrator_state)
   val, momenta, lp = leapfrog(val, momenta, direction * eps, integrator_state)
   weight = lp + assess_momenta(momenta)
 
-  return Tree((val, momenta, val, momenta, val, 1, weight, false))
+  diverging = weight - weight_init > 1000
+
+  return Tree(val, momenta, val, momenta, val, 1, weight, false, diverging)
 end
 
 function merge_trees(tree_left, tree_right)
@@ -67,26 +70,29 @@ function merge_trees(tree_left, tree_right)
   stop = tree_left.stop || tree_right.stop || u_turn(
     tree_left.val_left, tree_right.val_right, tree_left.momenta_left, tree_right.momenta_right
   )
+  diverging = tree_left.diverging || tree_right.diverging
 
-  return Tree((tree_left.val_left, tree_left.momenta_left, tree_right.val_right,
-    tree_right.momenta_right, sample, n, weight, stop))
+  return Tree(tree_left.val_left, tree_left.momenta_left, tree_right.val_right,
+    tree_right.momenta_right, sample, n, weight, stop, diverging)
 end
 
-function build_tree(val, momenta, depth, eps, direction, integrator_state)
+function build_tree(val, momenta, depth, eps, direction, weight_init, integrator_state)
   if depth == 0
-    return build_root(val, momenta, eps, direction, integrator_state)
+    return build_root(val, momenta, eps, direction, weight_init, integrator_state)
   end
 
-  tree = build_tree(val, momenta, depth - 1, eps, direction, integrator_state)
+  tree = build_tree(val, momenta, depth - 1, eps, direction, weight_init, integrator_state)
 
-  if tree.stop
+  if tree.stop || tree.diverging
     return tree
   end
 
   if direction == 1
-    other_tree = build_tree(tree.val_right, tree.momenta_right, depth - 1, eps, direction, integrator_state)
+    other_tree = build_tree(tree.val_right, tree.momenta_right, depth - 1, eps, direction,
+                            weight_init, integrator_state)
   else
-    other_tree = build_tree(tree.val_left, tree.momenta_left, depth - 1, eps, direction, integrator_state)
+    other_tree = build_tree(tree.val_left, tree.momenta_left, depth - 1, eps, direction,
+                            weight_init, integrator_state)
   end
 
   if direction == 1
@@ -96,6 +102,27 @@ function build_tree(val, momenta, depth, eps, direction, integrator_state)
   end
 end
 
+"""
+    (new_trace, sampler_statistics) = nuts(
+        trace, selection::Selection;eps=0.1,
+        max_treedepth=15, check=false, observations=EmptyChoiceMap())
+
+Apply a Hamiltonian Monte Carlo (HMC) update with a No U Turn stopping criterion that proposes new values for the selected addresses, returning the new trace (which is equal to the previous trace if the move was not accepted) and a struct `sampler_statistics` containing information about the sampled trajectory.
+
+The NUT sampler allows for sampling trajectories of dynamic lengths, removing the need to specify the length of the trajectory as a parameter.
+The sample will be returned early if the height of the sampled tree exceeds `max_treedepth`.
+
+`sampler_statistics` is a struct containing the following fields:
+    - depth: the depth of the trajectory tree
+    - n: the number of samples in the trajectory tree
+    - sum_alpha: the sum of the individual mh acceptance probabilities for each sample in the tree
+    - n_accept: how many intermediate samples were accepted
+    - accept: whether the sample was accepted or not
+
+# References
+Betancourt, M. (2017). A Conceptual Introduction to Hamiltonian Monte Carlo. URL: https://doi.org/10.48550/arXiv.1701.02434
+Hoffman, M. D., & Gelman, A. (2022). The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. URL: https://arxiv.org/abs/1111.4246
+"""
 function nuts(
   trace::Trace, selection::Selection; eps=0.1, max_treedepth=15,
   check=false, observations=EmptyChoiceMap())
@@ -105,12 +132,15 @@ function nuts(
     # values needed for a leapfrog step
     (_, values_trie, _) = choice_gradients(trace, selection, retval_grad)
     values = to_array(values_trie, Float64)
-    integrator_state = (values_trie, selection, retval_grad, trace)
 
     momenta = sample_momenta(length(values))
     prev_momenta_score = assess_momenta(momenta)
 
-    tree = Tree((values, momenta, values, momenta, values, 1, -Inf, false))
+    weight_init = prev_model_score + prev_momenta_score
+
+    integrator_state = (values_trie, selection, retval_grad, trace)
+
+    tree = Tree(values, momenta, values, momenta, values, 1, -Inf, false, false)
 
     direction = 0
     depth = 0
@@ -119,14 +149,16 @@ function nuts(
       direction = rand([-1, 1])
 
       if direction == 1 # going right
-        other_tree = build_tree(tree.val_right, tree.momenta_right, depth, eps, direction, integrator_state)
+        other_tree = build_tree(tree.val_right, tree.momenta_right, depth, eps, direction,
+                                weight_init, integrator_state)
         tree = merge_trees(tree, other_tree)
       else # going left
-        other_tree = build_tree(tree.val_left, tree.momenta_left, depth, eps, direction, integrator_state)
+        other_tree = build_tree(tree.val_left, tree.momenta_left, depth, eps, direction,
+                                weight_init, integrator_state)
         tree = merge_trees(other_tree, tree)
       end
 
-      stop = stop || tree.stop
+      stop = stop || tree.stop || tree.diverging
       if stop
         break
       end
@@ -147,12 +179,13 @@ function nuts(
     end
 
     # accept or reject
-    alpha = new_model_score - prev_model_score + new_momenta_score - prev_momenta_score
+    alpha = new_model_score + new_momenta_score - weight_init
     if log(rand()) < alpha
-      return (new_trace, Stats((depth, tree.n, true)))
+      return (new_trace, SamplerStats(depth, tree.n, true))
     else
-      return (trace, Stats((depth, tree.n, false)))
+      return (trace, SamplerStats(depth, tree.n, false))
     end
 end
 
-export nuts
+export nuts
+